Page 25 - Pra U STPM 2022 Penggal 2 - Mathematics

Mathematics Semester 2 STPM Chapter 4 Differential Equations

Exercise 4.2

Find the general solution of the following differential equations.

dy 1 dr 3 + t 2
1. = x + 2. =
2
dx x 2 dt t
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1 dy 1 dx
3. x dx = x – 1 4. x dt = t + 2
2
dy dy
5. = y – 4 6. x = –y 2
2
dx dx
dy 2 + y 2 dy
7. = 8. (x – 2) – y = 0
dx y dx
dy dy 1
9. x = xy + y 10. =
dx dx ye x
y 2 dy dy
11. x dx = ln x 12. x dx = 1 – 2y + y 2
dy dy
2
2
2
13. (y + 1) + 2xy = 2x 14. 2y – xy = x
dx dx
Solve the following differential equations.
dy y dy 1
15. = – 16. =
dx x dx x – 1
dy dy
2
17. = y + 2 18. (x – 2) – 2xy = 0
dx dx
dy dy
19. (x – 1) – y = 0 20. = 2xy + y
dx dx 4
Find the particular solution of the following differential equations with the given initial conditions.

dy dy 1
21. y = x + 2, y = 2 when x = 1 22. = + x, y = 1 when x = 1
dx dx x
dy dy 1 + x
23. = 2y – 3, y = 2 when x = 0 24. = , y = 1 when x = 2
dx dx x – 1
2
dy 2x dy 3y – 1
25. = , y = 0 when x = –1 26. = , y = 1 when x = –1
dx 1 + x 2 dx 6y
–x dy
27. e = 1, y = –1 when x = 0 28. xy dy = ln x, y = 0 when x = 1
dx dx
dy x + y dy
29. + y = 4, y = 0 when x = ln 2 30. e = x, y = 1 when x = 0
2
dx dx
dy dy

2
2
31. y = , y = 0 when x = 0 32. = x 9 , y = 9 when x = 0
x +

9 – 4y
dx dx
dy 1 e y dy x – 1
2
33. + = , y = ln 2 when x = 1 34. xy = , y = 0 when x = 1
dx x x dx y – 1
2 dy
35. (1 + x ) + 2xy = 4x, y = 0 when x = 1
dx
133

04 STPM Math(T) T2.indd 133 28/01/2022 5:44 PM